Small prismated tesseractic tetracomb

Small prismated tesseractic tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Spittit
Coxeter diagram	x4o3o3x4o ()
Elements
Tera	6N tesseracts, 4N cuboctahedral prisms, N rectified tesseracts, N small disprismatotesseractihexadecachora
Cells	16N tetrahedra, 32N triangular prisms, 4N+24N+24N cubes, 8N cuboctahedra
Faces	64N triangles, 24N+24N+96N squares
Edges	48N+96N
Vertices	32N
Vertex figure	Triangular antifastegium, edge lengths 1 (base edges of triangular prism) and √2 (all other edges)
Related polytopes
Army	Spittit
Regiment	Spittit
Conjugate	Quasiprismated tesseractic tetracomb
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	R5
Convex	Yes
Nature	Tame

The small prismated tesseractic tetracomb or spittit, also called the runcinated tesseractic tetracomb is a convex uniform tetracomb. 1 rectified tesseract, 2 small disprismatotesseractihexadecachora, 3 tesseracts, and 3 cuboctahedral prisms join at each vertex of this tessellation. As the name suggests, it is the runcination of the tesseractic tetracomb.

Vertex coordinates

The vertices of a small prismated tesseractic tetracomb of edge length 1 are given by all permutations of:

• $\left(\pm {\frac {1}{2}}+(1+{\sqrt {2}})i,\,\pm {\frac {1}{2}}+(1+{\sqrt {2}})j,\,\pm {\frac {1}{2}}+(1+{\sqrt {2}})k,\,\pm {\frac {1+{\sqrt {2}}}{2}}+(1+{\sqrt {2}})l\right)$,

where i , j , k , and l  range over the integers.

Representations

A small prismated tesseractic tetracomb has the following Coxeter diagrams:

• x4o3o3x4o () (full symmetry)
• x3o3o4x *b3x () (half symmetry)

External links

• Klitzing, Richard. "spittit".
• Wikipedia contributors. "Runcinated tesseractic honeycomb".